How to animate a tesseract
Another way is to use combination of modifiers:


Create a plane, offset its origin;
Hook the whole plane to a new empty object (CtrlH);
Add a Screw modifier, set step to 4, rotate the two objects 45° along global Z;
Add a Lattice, which is used to tweak the shape;
Add a Wireframe modifier;
Animate by rotating along local X (or Y, Z) of that empty object.




Example File